MINISTRY OF EDUCATION AND TRAINING HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION VO NGOC YEN PHUONG “STUDY ON THE QUASI-ZERO STIFFNESS VIBRATION ISOLATION SYSTEM” MAJOR: MECHANICAL ENGINEERING MAJOR CODES: 9520103 THE DOCTORAL THESIS Ho Chi Minh City, Oct./ 2022 MINISTRY OF EDUCATION AND TRAINING HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION VO NGOC YEN PHUONG “STUDY ON THE QUASI-ZERO STIFFNESS VIBRATION ISOLATION SYSTEM” MAJOR: MECHANICAL ENGINEERING MAJOR CODES: 9520103 SCIENTIFIC SUPERVISORS: 1. Le Thanh Danh 2. Nguyen Minh Ky 1. Reviewer 3: Ho Chi Minh City, Oct./ 2022 ORIGINALITY STATEMENT “I hereby declare that this submission is my own work, done under the supervision of Assoc.
Le Thanh Danh and Dr. Nguyen Minh Ky and all the best of my knowledge, it contains no illegal materials previously published or written by another person.” Ho Chi Minh City, Oct. 10 th 2022 Vo Ngoc Yen Phuong i ACKNOWLEDGEMENT This dissertation was put down in writing from 2018 to 2021 during my time as a Doctor of Philosophy Candidate at the Mechanical Engineering Faculty at Ho Chi Minh City University of Technology and Education. I would like to express my deep gratitude to Assoc.
Le Thanh Danh for bestowing me the opportunity to take part in his research group as well as for his conscientious instruction as my principal doctoral mentor. Simultaneously, he let me experience my independent study and he always supervised carefully during my research schedule. Besides, I also want to thank Dr. Nguyen Minh Ky from the Faculty of Mechanical Engineering of HCMC University of Technology and Education for his devotion as a co- supervisor for my PhD thesis.
I would like also to acknowledge the National Foundation for Science and Technology Development (NAFOSTED, Vietnam) and Ho Chi Minh City University of Technology and Education for their financial assistance throughout my research project. Thanks to their interest, this thesis has been accomplished on time. I am really grateful to my colleagues at Mechanical Engineering Faculty at Industrial University of Ho Chi Minh City for their friendly supports. In addition, I would like to appreciate the lecturers at Mechanical Engineering Faculty at University of Technology and Education for their meaningful assistance.
Finally, I express my thanks to my family, especially my mother, my husband and my two daughters for their emotional encouragement throughout my study. Ho Chi Minh City, Oct. / 2022 Vo Ngoc Yen Phuong ii ABSTRACT The thesis of “Study on the quasi-zero stiffness vibration isolation system” is presented in six chapters. The thesis introduces an innovation quasi -zero stiffness adaptive vibration isolation model (QSAVIM) composed by semicircular CAM-wedge-pneumatic spring mechanism.
One with the positive stiffness including the wedges, the rollers and the two rubber air springs, is used to support the load. The other comprising the semi-circular cams, the rollers and other air springs, whose stiffness is negative, is employed to adjust the system stiffness. In this model, a component which is non-steel elastic element is the pneumatic spring including rubber air spring and pneumatic cylinder are employed respectively in the proposal model. The restoring model of a commercial rubber air spring is analyzed and developed, which is contributed by three factors including compressed air, friction and viscoelasticity of the rubber bellow.
Herein, the nonlinear hysteresis model of the rubber tube is also considered. Then, an experimental rig is set up to identify and verify the parameters of the rubber air spring model. In addition, the friction force of the pneumatic cylinder is also investigated through using virtual prototyping technology. The complex nonlinear dynamic response of the quasi-zero stiffness adaptive vibration isolation model which is a parallel connection between a load bearing mechanism and a stiffness corrected one is realized.
The important feature of the proposed model is that it is easy not only to adjust the stiffness to adapt according to the change of the isolated mass but to improve the isolation effectiveness in low frequency region that is useful in practical application. The studied results show that the effectiveness of the proposed model is much better than the equivalent traditional model. iviii CONTENTS OF THESIS Cover page Page Originality statement.v List of figures .vi List of tables.viii CHAPTER 1: INTRODUCTION……………………………………………………….1 The necessity of vibration isolation……………………………….2 The aim of the research……………………………………………….3 The problems are needed solutions…………………………………….4 Research scope and object…………………………….6 Contents of thesis ……………………………………………………….7 Organization of thesis……………………………………………………14 1.8 The obtained results……………………………………………….9 The scientific and application contribution of the thesis…………….15 SUMMARY OF CHAPTER 1………………………………………….15 CHAPTER 2: LITERATURE REVIEWS ………………………………………………. Models of proposed vibration isolation………………………………….
Isolated model using Euler spring…………………………………. Isolated model featuring quasi-zero stiffness characteristic……….21 SUMMARY OF CHAPTER 2……………………………………………….…38 CHAPTER 3: FUNDAMENTAL OF RELATIVE THEORIES…………………………….2 General structure of rubber bellow…………………………………. Mathematical model of the compressed air………………………………. Frictional model of pneumatic cylinder and rubber material………….
Frictional model of pneumatic cylinder……………………………43 3. Frictional model of rubber material………………………………. Viscoelastic model of the rubber material………………………………. Normal form method……………………………………………………….
Multi scale method……………………………………………………. Runge-kutta method………………………………………………………. Brief introduction of Genetic Algorithm………………………………….53 SUMMARY OF CHAPTER 3………………………………………………….55 CHAPTER 4: QUASI-ZERO STIFFNESS VIBRATION ISOLATOR USING A RUBBER AIR SPRINGS……………………………………………………………………………. Mechanical model of isolator…………………………………………………….
Restoring model of a rubber air spring………………………………….1 Compressed air force………………………………………………. Model identification and verification results……………………. Static analysis of the isolator …………………………………………. Analysis of equilibrium position……………………………….
Equation of vibration transmissibility…………………………. Effects of configurative parameters on vibration transmissibility curve.1 Influence of pressure ratio on the shape of the amplitude-frequency response curve…………………………………………………………88 4.2 Influence of geometrical parameters on the resonant peak…….3 Effects of damping on vibration transmissibility curve……………93 4. Complex dynamic analysis………………………………………………. Frequency jump phenomenon………………………………………95 4.
Dynamic response under random excitation………………. Design procedure for obtaining quasi-zero stiffness isolator………….8 Experimental result and apparatus………………………………….105 SUMMARY OF CHAPTER 4………………………………………………….112 CHAPTER 5: QUASI-ZERO STIFFNESS VIBRATION ISOLATOR USING A PNEUMATIC CYLINDERS………………………………………………………………. Model of QSAVIM using a PC…………………………………………. Pneumatic cylinder with auxiliary chamber………………………….
Stiffness of the modified model……………………………………….4 Stiffness analysis of the LBM and SCM……………………………….5 Stiffness analysis of the modified model………………………………….6 The analysis of equilibrium position…………………………………. Frequency-amplitude relation…………………………………. Stability of the steady state solution………………………………156 5. Transmissibility for force excitation………………………………156 5.
Influence of parameters on the force transmitted curve………. Complex dynamic analysis……………………………………….165 SUMMARY OF CHAPTER 5…………………………………………….…175 CHAPTER 6: CONCLUSIONS AND FUTURE WORKS ……………………………….………182 Reference………………………………………………………………………………………184 iv NOMENCLATURE Latin letters A Area of the cylinder in m2 Ae Effective area of the rubber air spring in m2 Awh Effective area of the rubber air spring at the working height in m2 Cd Damping coefficient in Ns/m cp Specific heat capacity at constant pressure cv Specific heat capacity at constant volume D Dissipation function d Distance between the base and the DSEP in mm Ek Kinetic Energy in Joule Ep Potential Energy in Joule F Force in N Fair Air compressed force in N Fap Approximate force in N Fc Coulomb friction force in N Ffri Frictional force inside rubber material in N Fst Static friction force in N Fg Gravity force in N Fras Force of rubber air spring in N Fs Restoring force in N Fsf Sliding frictional force between piston and cylinder in N Fvie Viscoelastic force in N FLMB Restoring force of load bearing mechanism in N v FSCM Restoring force of stiffness corrected mechanism in N Fs Restoring force of the QSAVIM in N fe External force in N Gin Mass low rates at inlet in kg/s Gout Mass low rates at outlet in kg/s g Acceleration of gravity in m/s2 Ho Static vertical deformation of the QSAVIM in mm h Height of the cylinder in mm J Cost function Kair Compressed air stiffness in N/m KDSEP Stiffness at the DSEP in N/m KSCM Stiffness of the SCM in N/m KLBM Stiffness of the LBM in N/m mair Mass of the air in the pneumatic working chamber in kg M Mass of the isolated object in kg n Ratio of specific heat capacity. ns Exponent of the Stribeck curve P Pressure in N/m2 Patm Atmosphere pressure in N/m2 Pwh Pressure of the rubber air spring at the working height in N/m2 Pac Pressure of air in the auxiliary chamber Pcy Pressure in pneumatic cylinder Pso Pressure in the cylinder at the initial position v Q Generalized force R Radius of the semicircular cam in mm Rair Gas constant in J/Kg.K r Radius of the roller in mm T Temperature of the air in the pneumatic working chamber in K Ta Displacement transmissibility TF Force Transmissibility u Relative displacement between then center of the cam and DSEP in mm Vr Relative velocity between two contacting surfaces in m/s vs Stribeck velocity in m/s V Volume in m3 Ve Effective volume in m3 Vac Volume of auxiliary chamber Vcy Volume of cylinder Vwh Effective volume of the rubber air spring at the working height in m3 Vd Volume of the cylinder at the working height in m3 x Displacement of one end of the rubber air spring or cylinder in mm xwh Deformation of the rubber air spring at the working height in mm ze Excitation in mm z Absolute displacement of the isolated object in mm Z Absolute vibration amplitude of the isolated object in mm Greek letters α Angle of the wedge in degree , Phase angle between u and ze v Phase angle between z and ze µ Pressure ratio ω Excitation frequency in rad/s ωn Natural frequency in rad/s α ht Heat transfer coefficient a the heat transfer surface area the viscous friction coefficient, Damping ratio L Vertical displacement of the load plate Subscripts ac Auxiliary chamber atm Atmosphere cy Cylinder e Excitation ef External force F Force k Kinetic LBM Load bearing mechanism p Potential SCM Stiffness corrected mechanism ras Rubber air spring s Spring sf Sliding force v r Relative vie Viscoelasticity wh Working height Superscripts -or Dimensionless quantity Time derivative Dimensionless time derivative v LIST OF FIGURES Fig. A conventional vibration isolation system [4] 17 Fig.
The transmissibility curve of the conventional vibration isolation 18 system Fig. A model of low frequency vibration isolation [5] 19 Fig. A QZS vibration isolation model for low frequency in vertical 20 direction [6] Fig. A simple structure for mounting and constraining Euler springs [7] 20 Fig.
A QZS vibration isolation model for low frequency [8] 21 Fig. Dynamical model with low frequency comprising a vertical and a 22 pair of oblique springs Fig. Simple model of a nonlinear isolator that behaves as a Duffing 22 oscillator at low amplitudes of excitation Fig. Scheme of QZS vibration isolator 23 Fig.
Proposed isolation system using Euler buckled beams with bar 23 connected to the seat and (b) detailed part of the seat. Schematic model of Quasi-zero stiffness isolator with Coulomb 24 Damping. Simplified mechanical analysis model of the five-spring QZS 24 vibration isolator (this position is just the static equilibrium position) Fig. Mechanism of the proposed translational-rotational QZS structure: 25 (a) the initial condition, (b) with force and moment applied Fig.
Three-dimensional vibration isolation diagram: (1) base, (2) 25 support column, (3) a skateboard, (4) a connecting rod, (5) stage, (6) vertical springs, (7) slider, and (8) tension spring; (b) 3D- vi modeling of the vibration isolator: (9) isolated objects and (10) rollers Fig. A QZS vibration isolation model for low frequency as designed in 26 [19-20] Fig. Vibration isolator with time delayed active control strategy [21] 27 Fig. (a) Schematic diagram of local resonant sandwich plate; (b) The 28 unit cell of the spring mass system; (c) Two degrees of freedom „spring-mass‟ model of the plate-type elastic metamaterial.
Design of toe-like vibration isolator for vibration isolation in 28 vertical direction inspired by the toe. Bionic model of a variable stiffness vibration isolated joint [24] 29 Fig. The model of the GAS isolator. (a) Schematic diagram of the GAS 29 isolator Fig.
Stewart vibration isolator 30 Fig. Isolated model proposed by Y. Zheng et al. Configuration of MNSI based on Maxwell magnetic normal stress.
31 (a) Cross-section view of isolator; (b) Configuration of excitation mechanism Fig.24 Configuration of isolator designed by [29] 31 Schematic diagram of the multi-direction isolator.